In article <gjqgt0tetd3vkpkkoe3cb8dvncpemuahnv@4ax.com>, kalanamak wrote:> The text I'm using on teaching children math forbids the use of "goes> into" when talking about division. They say it is "meaningless". For the> problem 427/62, they advise the child think aloud along the lines of> 1) can 6 tens and 2 ones be subtracted from 4 tens and 2 ones? No. Can 6> tens and 2 ones be subtracted from 4 hundreds and 2 tens? Yes. How many> times? etc..> OR> 2) How many groups of 62 can I make out of 427 objects?> > Is this proper or farfetched? If the above is farfetched, is "goes into"> still commonly used, or, if not, what is used?> I am not clear from the text how the child goes about answering the 'how> many times' or 'how many groups' question. Trial and error? Estimation> and best guess first?

I don't know what elementary teachers now teach (mine tried hard toavoid "goes into" 40 years ago, so it isn't a new prejudice).

Actually there is nothing inherently wrong with the "goes into" operator.You can define it easily and unambiguously: a "goes into" b =def b / aIt is not meaningless, just non-standard.

So far as I can tell, this operator is still used in speech (usuallypronounced "guzinta" around here), but not in writing---there is nostandard symbol for it.

The long-division algorithm has always suffered from the need to guesshow many times the divisor goes into the current part of the dividend.If you guess low, you'll end up with a remainder that is too big, andhave to increment your guessed digit. If you guess high, you'll endup with a negative remander and have to decrement your guessed digit.Unfortunately, the algorithm is usually presented as if people alwaysguessed perfectly, losing a great apportunity to teach how to recoverfrom mistakes---a useful skill later on when dealing with morecomplicated algorithms.